What is the binary representation of the following hexadecimal number? What are the decimal numbers they represent when interpreted as undesigned integers.
(a) F4
(b) 9F
A hexadecimal digit can take up to 16 values, from 0 to 15. In order to represent values beyond 9 in one single digit, the digits A,B,C,D,E,F are used to represent 10,11,12,13,14,15 respectively.
Since we can also express 0 to 15 in 4 binary digits, there is a frequent need for conversion between hex and binary digits. Here is a conversion table:
hex binary
0 0
1 1
2 10
3 11
4 100
5 101
6 110
7 111
8 1000
9 1001
A 1010
B 1011
C 1100
D 1101
E 1110
F 1111
So E6 can be converted to binary digit by digit by combining E=1110 and 6=0110 into 11100110.
You can read more about the subject here:
http://en.wikipedia.org/wiki/Hexadecimal
On your PC you have good calculator.
Start�¨Programs�¨Accessories�¨Calculator
When you open Calculator clik on View, then click Scientific.In up left angle you have numbers systems Hex Dec Oct and Bin. Click Hex.Use numbers and letters in down right angle to type some hexadecimal number. Then in up left angle click for some of numbers system and you representation.
You will see representation of this nuber in some other numbers system.
To convert a hexadecimal number to binary, you need to understand the relationship between the two number systems. The hexadecimal system uses base 16, while the binary system uses base 2.
To convert a hexadecimal digit to its binary equivalent, you can use the following conversion table:
Hexadecimal | Binary
------------|-------
0 | 0000
1 | 0001
2 | 0010
3 | 0011
4 | 0100
5 | 0101
6 | 0110
7 | 0111
8 | 1000
9 | 1001
A | 1010
B | 1011
C | 1100
D | 1101
E | 1110
F | 1111
Let's now convert the hexadecimal numbers to binary:
(a) F4:
To convert F4 to binary, we can use the table provided.
F in binary is 1111, and 4 in binary is 0100.
So, F4 in binary is 11110100.
To interpret this binary number as an unsigned integer, you can convert it back to decimal by using the binary positional notation. Each bit represents a power of 2 from right to left.
11110100 in decimal is calculated as follows:
(1 * 2^7) + (1 * 2^6) + (1 * 2^5) + (1 * 2^4) + (0 * 2^3) + (1 * 2^2) + (0 * 2^1) + (0 * 2^0)
= 128 + 64 + 32 + 16 + 0 + 4 + 0 + 0
= 244
So, the hexadecimal number F4 represents 244 in decimal when interpreted as an unsigned integer.
(b) 9F:
Using the conversion table, we can convert each hexadecimal digit to binary.
9 in binary is 1001, and F in binary is 1111.
So, 9F in binary is 10011111.
To interpret this binary number as an unsigned integer, we use the same method as before.
10011111 in decimal is calculated as follows:
(1 * 2^7) + (0 * 2^6) + (0 * 2^5) + (1 * 2^4) + (1 * 2^3) + (1 * 2^2) + (1 * 2^1) + (1 * 2^0)
= 128 + 0 + 0 + 16 + 8 + 4 + 2 + 1
= 159
Therefore, the hexadecimal number 9F represents 159 in decimal when interpreted as an unsigned integer.